# How can early people prove that their planet is a cuboid?

Imagine a cuboid planet with a thick atmosphere orbiting a star similar to our Sun. The inhabitants are as intelligent as humans and recently discovered the universal laws of gravitation and motion which are familiar to us. How can they determine that the planet is a cuboid? The dimension is 1024 cubic kilometers and for some unknown reasons the cuboid planet is formed and has remained that way ever since.

I'm looking for primitive technology to prove the planet is a cuboid with the specified dimensions with smallest error margin possible.

The stated dimensions (1024 cubic kilometers) is a cube about 10 km on a side. Sophisticated technology wouldn't be necessary, they could walk the sides of the "planet". (To be clear with the nomenclature, nothing with a longest-axis of 17 km is a "planet", it's just a large asteroid. The threshold for "planet" according to the IAU is a 2000 km diameter.)

Aside from that, the continued existence of a cuboid planet is impossible (assuming gravity and matter work the way they do in our universe) as detailed in this answer:

The problem is that objects on a planetary scale don't behave the same as boulder or even small moon sized things. Anything above 200-300km radius squishes into a spherical shape.

And discovery of the shape of their world would be very similar to determining a flat earth, as detailed in this answer.

• the continued existence of a cuboid planet is impossible umm... not when the size of the 'planet' is so low its gravity is more likely to be in the 1e-3g range and the chance of a molten core is nil. A tough rock will stay like this for eons. – Adrian Colomitchi Mar 6 '20 at 0:44
• @AdrianColomitchi Well, sure, but at that size it's not a "planet". Pluto's two hundred times the size of the proposed space rock, and it's not a planet. Anything big enough to rate as a "planet" is going to be spherical barring magic handwavium. – jdunlop Mar 6 '20 at 0:47
• True. This is why I used quotes around 'planet' - one cannot truly call it that way. Asteroid is more likely. – Adrian Colomitchi Mar 6 '20 at 0:53
• Actually no cuboid regardless of size is a planet, the shape is part of the definition. – Ville Niemi Mar 6 '20 at 7:08

I don't think its possible to have a cubic planet with an atmosphere as gravity would crush the edges, form a molten surface and become round again. You also run into huge issues with water, some sides being cast in a permanent shadow and air flow due to the cubic mountain ridges.

But from a technology stand point, it should be pretty easy using the same length stick and measure the shadows at various locations to determine if the surface of the planet is flat. That's how the Egyptians essentially determined the world was round and they hadn't even figured out gravity.

You would have also had early sailors note that the entire planet was surrounded by an impassible mountain range, the height of which would be far too high for people to pass. (The atmosphere and water on the planet would be circular due to gravity, but it's a cube, so you would have to have massive mountain ranges extending out of the atmosphere.)

Aristoteles proved the earth was round several millenia ago, by looking at the shadow the earth casts on the moon during lunar eclipses. If your planet has a similar moon to earth, then you can determine the shape. Considering the earth is spinning, each lunar eclipse would five you a little more info, until you had the right idea eventually.

a 90 degree cliff that you can then vector around is a pretty big one, i like the idea of a waterfall that "falls down" on 4 of those faces continually, but think of what rolling a ball "down" each of the 3 faces of a corner would look like.

an Engineered cube of planatoid size would basically just have 8x three faced peaks around a core. you can take this from sphere all the way to flat faced cube, with more and more weirdness on water features wanting to spherize in spite of the geo or other features. Lakes would want to pull away from those corners in an otherwise normal physics space, but if one was to go down the discworld or other flat space ideas, then you could just play up the hard corner's

(now i'm imagining 6 different tribes that only recently braved searching out the other "faces" of a space... walking to an edge and then flipping around it, versus falling in THEIR "down" and bouncing off of stuff ad infinitum...)